Species immigration, extinction and turnover of vascular plants in boreal lakes
Dictated by limited resource availability for land acquisition, a central question in conservation biology is the ability of areas of different size to maintain species diversity. The selected reserves should not only be species rich at the moment, but should also maintain species diversity in the long run. We used two sets of data on vascular plant species in boreal lakes collected in 1933/34 and 1996 to test the relationships between lake area and the extinction, immigration and turnover rates of the species. Moreover, we investigated, whether the number of species in 1933/34 or water connection between lakes was related to extinction, immigration and turnover rates of species. We found that lake area or shoreline length was not correlated with immigration or turnover rate. But extinction rate was slightly negatively correlated with shoreline length. The original number of species was positively related to the number of species extinctions and to the absolute turnover rate in the lakes, which indicates that species richness does not create stability in these communities. Species number was not correlated with immigration rate. Upstream water connections in the lakes did not affect immigration, extinction or turnover rates. We conclude that length of the shoreline is a better measure of suitable area for water plants than the lake area, and that because the correlation between shoreline length and extinction rate was slight, also small lakes can be valuable for conservation.
- Research Article
100
- 10.2307/3545388
- Mar 1, 1992
- Oikos
Relationships between local annual immigration and extinction rates of plant species and total species richness were determined from long-term data in permanent plots in tallgrass and shortgrass prairies in Kansas. Combining plots resulted in higher equilibrium numbers of species as predicted from immigration and extinction rates. Immigration and extinction rates also increased with scale. Extinction rates are higher because the regional scale supports more rare species which, in turn, have high probabilities of extinction. We also tested the hypotheses that extinction rates would be higher on burned versus unburned grasslands, and that immigration rates would be higher on grazed versus ungrazed grasslands. Extinction rates were positively correlated with the number of species at a site, and this relationship was not altered by burning or grazing. Immigration rates were variable, but were sometimes positively correlated with growing season precipitation. Immigration rates decreased in years sites were burned. Therefore, after fire, the number of species going locally extinct was still dependent on earlier species richness, but the number of species added to the site was reduced. Variances in immigration and extinction rates were high, therefore, confident predictions regarding the effects of burning or grazing regimes on species richness could not be made. Variance in rates of immigration and extinction results in a range of values within which the equlibrium number of species fluctuates randomly.
- Research Article
73
- 10.1111/jbi.12064
- Jan 25, 2013
- Journal of Biogeography
AimMacArthur and Wilson's theory of island biogeography was revolutionary, and also inspired the more recent unified neutral theory of biodiversity and biogeography. The unified neutral theory has the potential to make predictions about island biogeography that are not well studied. Here we aim to unify the two theories by using an ecological neutral model to study immigration and extinction rates on islands – the cornerstone of MacArthur and Wilson's theory.MethodsWe conduct simulations of a spatially implicit neutral model and measure species abundances, immigration rates and extinction rates. We study the behaviour of the model at dynamic equilibrium and on approach to dynamic equilibrium both from volcanic origin (low initial diversity) and from land bridge origin (high initial diversity). We extend the model to study the effects of clustered immigration and to explicitly account for the distinction between immigration and colonization.ResultsOur model, in accord with the simplest version of MacArthur and Wilson's theory, predicts linear immigration and extinction rates as functions of species richness at dynamic equilibrium. In contrast, the approach to dynamic equilibrium produces rich and unexpected behaviour where immigration and extinction rates are non‐monotonic functions of species richness, at odds with other theory. Once examined, however, this behaviour makes biological sense and results from the influence of the species abundance distribution over immigration and extinction rates. The turnover predicted by our first model appears high, but can be lowered to realistic levels with an alternative model of clustered immigration or by accounting for the difference between the immigration of a new species and its true colonization of the island.Main conclusionsMacArthur and Wilson's theory of island biogeography and ecological neutral theory are different, but there are strong similarities in their assumptions and predictions that should not be overlooked when evaluating them. Our results highlight the importance of species abundances as indicators of immigration and extinction rates; species richness alone is insufficient. In particular, extinction rate and species abundances are unavoidably linked, as rarity usually precedes extinction.
- Research Article
24
- 10.2307/2680234
- Aug 1, 2001
- Ecology
Stream landscapes are highly variable in space and time and, like terrestrial landscapes, the resources they contain are patchily distributed. Organisms may disperse among patches to fulfill life-history requirements, but biotic and abiotic factors may limit patch or locality occupancy. Thus, the dynamics of immigration and extinction determine, in part, the local structure of assemblages. We sampled fishes and stream habitat at 12 localities for two years (96 samples) to examine the deterministic nature of immigration and extinction processes in stream fish assemblages. Mean immigration rates for assemblages were highest at large stream localities, where the pool of potential immigrants was largest. Mean extinction rates were highest where variability in the flow regime was high, though local refugia appeared to modify the extinction process at one locality. Significant nested subset patterns in species composition occurred over time for 7 of the 12 localities. The strength of the nesting was associated with mean immigration and extinction rates. Higher extinction rates corresponded to stronger nestedness, whereas higher immigration rates were associated with weaker nestedness. Across all species, both immigration and extinction rates were strongly associated with mean abundance. Species with high local abundances had higher immigration rates and lower extinction rates than did species with low local abundances. There were no significant associations between trophic guild or body size and immigration and extinction rate. This work supports the hypothesis that immigration and extinction rates for assemblages are predictable along environmental gradients, and that species are less prone to local extinction and more prone to colonize areas when they maintain high local abundances. The extinction process in local assemblages can be a highly ordered event leading to strong nested subset patterns, but immigration appears to be more stochastic.
- Research Article
46
- 10.1071/bt9770193
- Jan 1, 1977
- Australian Journal of Botany
In 1975 lists were made of the plant species occurring on 121 limestone islands, varying from 3 m2 to 160,900 m2 in area, west of Perth. Fifty-four of the islands supported no vascular plant species. An explanation of the different number of plant species found per island (S) was sought in terms of island area (A), elevation (E), and diversity of habitat types (H). Significant linear correlations were found between S and A, S and E, and S and H. The validity of neglecting islands with zero species number in regression analyses was evaluated and found to be wanting. Small islands (area < 5000 m2) tend to have impoverished floras; a study of the exceptions shows that the impoverishment is mainly due to exposure to sea spray. Inter-island distance plays a negligible part in determining the similarities of island floras. Comparisons of the present flora lists for 20 islands with those made by G. M. Storr in 1956 or 1959 show that species turnover has occurred. Although 12 islands show an increase in plant species number (as total plants, perennials, annuals and native species), this tendency is not significant. Annual species have higher extinction rates than perennial species and alien species higher ones than native species. Alien species also have higher immigration rates than native species. Floras of islands with cormorant colonies tend to have higher extinction rates than islands without. Islands with gull rookeries have higher immigration rates of alien species than islands without. Considering all 20 islands together there are no significant differences between extinction and immigration rates. These rates are independent of island area and isolation respectively. It is suggested that seabird colonies override the importance usually ascribed to island area and isolation in influencing these rates.
- Research Article
126
- 10.1007/s00442-003-1353-x
- Sep 23, 2003
- Oecologia
Temporal dynamics of insect communities in terrestrial habitat fragments have been rarely studied. Here it was tested whether immigration, extinction, and turnover of butterfly species change with area and isolation of 31 calcareous grasslands. The area ranged from 0.03 to 5.14 ha, the isolation index from 2,100 to 86,000 (edge-to-edge distance 55-1,894 m). In both study years (1996, 2000), the total number of individuals (16,466, 15,101) and species (60, 54) sampled across all sites were similar and number of species increased with area in both years indicating an equilibrium. Rates of extinction (38% for habitat specialists vs. 20% for generalists) and turnover (51% vs. 35%) were higher, and rates of immigration (11% vs. 30%) were lower for habitat specialists than for generalists. Extinction and turnover rates decreased with increasing fragment size for both specialist ( n=25 species) and generalist ( n=36) butterflies, but specialists showed a significantly steeper decrease with increasing fragment size than generalists. Immigration rates increased with area. As a result, species number of habitat specialists declined in small habitats but not in large habitats between 1996 and 2000. No significant impact of habitat isolation on the butterfly community was found. The data suggest that large habitat fragments are of special importance for the conservation of the specialized, most endangered butterfly species. Habitat isolation appears to be less important, as butterflies can cope with the habitat mosaic in our study region.
- Research Article
6
- 10.1086/695849
- Nov 27, 2017
- Freshwater Science
Dispersal processes, such as immigration and extinction rates, and habitat properties play a crucial role in determining species composition and nestedness patterns within communities. In the current global scenario of changing environmental conditions and habitat fragmentation, information on the role of natural dispersal mechanisms and disturbance factors are especially important for understanding dynamics of species composition changes in stream ecosystems. We investigated spatial and temporal patterns of nestedness of fish communities in tropical stream systems of central India and the relationship of various dispersal factors (immigration–extinction rates and their variability) with habitat properties (habitat size and heterogeneity) and anthropogenic disturbances. We tested predictions of the classical model by Schlosser on immigration–extinction dynamics along longitudinal gradients in stream community composition for these streams. The results revealed significant patterns of nestedness for all study sites. Sites exposed to varying degrees of disturbance (induced by human activities) showed lower nestedness than undisturbed ones. Immigration rates did not show strong relations with nestedness but extinction rates were significantly related (negatively) to nestedness. In addition, disturbance played an important role in determining immigration rates and variability in immigration rates. Stream characteristics, such as habitat-size and habitat-variability gradients, were not statistically significant predictors of immigration and extinction rates. Our results demonstrate the influence of local anthropogenic disturbances on dispersal dynamics of species. A reduction in availability of suitable habitats could lower immigrations.
- Research Article
33
- 10.1111/j.1365-2427.2009.02335.x
- Apr 13, 2010
- Freshwater Biology
Summary1. Species richness in a habitat patch is determined by immigration (regional) and extinction (local) processes, and understanding their relative importance is crucial for conservation of biodiversity. In this study, we applied the Island Biogeography concept to spring ponds connected to a river in southwestern Japan to examine how immigration and extinction processes interact to determine fish species richness in temporally variable environments.2. Fish censuses were conducted 15 times in 13 study ponds at 1–4 month intervals from August 1998 through October 2000. Effects of habitat size (pond area), isolation (distance from the river) and temporal environmental variability (water level fluctuation) on (i) species richness, (ii) immigration and extinction rates and (iii) population size and persistence of each fish species were assessed.3. The results revealed predominant effects of distance on species richness, immigration/extinction rates and population size and persistence. Species richness decreased with increasing distance but was not related to either pond area or water level fluctuation. A negative effect of distance on immigration rate was detected, while neither pond area nor water level fluctuation had significant effects on extinction rate. Further, population size and persistence of four species increased with decreasing distance, suggesting that, in ponds close to the river, immigrants from the river reduce the probability of extinction (i.e. provide a rescue effect), contributing to the maintenance of high species richness.4. Overall results emphasise the importance of immigration processes, rather than extinction, in shaping patterns of species richness in our system. The predominant importance of immigration was probably because of (i) high temporal variability that negates habitat‐size effects and (ii) continuous immigration that easily compensates for local extinctions. Our results suggest that consideration of regional factors (e.g. connectivity, locations of source populations and barriers to colonisation) is crucial for conservation and restoration of local habitats.
- Research Article
79
- 10.1371/journal.pone.0039762
- Jun 29, 2012
- PLoS ONE
Global nitrogen (N) deposition and climate change have been identified as two of the most important causes of current plant diversity loss. However, temporal patterns of species turnover underlying diversity changes in response to changing precipitation regimes and atmospheric N deposition have received inadequate attention. We carried out a manipulation experiment in a steppe and an old-field in North China from 2005 to 2009, to test the hypothesis that water addition enhances plant species richness through increase in the rate of species gain and decrease in the rate of species loss, while N addition has opposite effects on species changes. Our results showed that water addition increased the rate of species gain in both the steppe and the old field but decreased the rates of species loss and turnover in the old field. In contrast, N addition increased the rates of species loss and turnover in the steppe but decreased the rate of species gain in the old field. The rate of species change was greater in the old field than in the steppe. Water interacted with N to affect species richness and species turnover, indicating that the impacts of N on semi-arid grasslands were largely mediated by water availability. The temporal stability of communities was negatively correlated with rates of species loss and turnover, suggesting that water addition might enhance, but N addition would reduce the compositional stability of grasslands. Experimental results support our initial hypothesis and demonstrate that water and N availabilities differed in the effects on rate of species change in the temperate grasslands, and these effects also depend on grassland types and/or land-use history. Species gain and loss together contribute to the dynamic change of species richness in semi-arid grasslands under future climate change.
- Research Article
6
- 10.1111/gcb.70334
- Jul 1, 2025
- Global change biology
The warming global climate is threatening terrestrial ecosystem stability, including plant community structure and diversity. However, it remains unclear how distribution, richness, and turnover of plant species are impacted by warming and wetting in northern China. In the present study, species distribution models were applied to predict the spatial distribution of 5111 plant species based on 111,071 occurrence records in northern China. Additionally, variations in species richness and turnover rates were predicted for 2100 under 3 scenarios. The results indicated that approximately 70% of plant species will expand in their distribution, resulting in an increase in species richness. These changes will be driven mainly by temperature seasonality (TSN), annual precipitation (MAP), and mean temperature of the coldest quarter (MTCQ). However, about 30%-40% of the species will face extinction risks, including a considerable number of endemic and Red-Listed species, and suitable habitat loss (LSH) will exceed 30%. Narrow-ranging species will be more likely to lose a larger percentage of their suitable habitats than wide-ranging species, highlighting their sensitivity to environmental changes. Importantly, it emerged that species turnover rates will increase linearly with ecological vulnerability at the grid level, indicating that community structure and species composition are easily affected by climate change in ecologically vulnerable areas. Therefore, biodiversity hotspots with high species richness in the southern study areas, as well as regions exhibiting both fast species turnover and significant ecological vulnerability, should be prioritized for conservation. These findings provide insights into how species composition and richness in plant communities vary with global climate change and provide effective ecological conservation and management strategies.
- Research Article
226
- 10.1890/0012-9658(2001)082[2320:discos]2.0.co;2
- Aug 1, 2001
- Ecology
Stream landscapes are highly variable in space and time and, like terrestrial landscapes, the resources they contain are patchily distributed. Organisms may disperse among patches to fulfill life-history requirements, but biotic and abiotic factors may limit patch or locality occupancy. Thus, the dynamics of immigration and extinction determine, in part, the local structure of assemblages. We sampled fishes and stream habitat at 12 localities for two years (96 samples) to examine the deterministic nature of immigration and extinction processes in stream fish assemblages. Mean immigration rates for assemblages were highest at large stream localities, where the pool of potential immigrants was largest. Mean extinction rates were highest where variability in the flow regime was high, though local refugia appeared to modify the extinction process at one locality. Significant nested subset patterns in species composition occurred over time for 7 of the 12 localities. The strength of the nesting was associated with mean immigration and extinction rates. Higher extinction rates corresponded to stronger nestedness, whereas higher immigration rates were associated with weaker nestedness. Across all species, both immigration and extinction rates were strongly associated with mean abundance. Species with high local abundances had higher immigration rates and lower extinction rates than did species with low local abundances. There were no significant associations between trophic guild or body size and immigration and extinction rate. This work supports the hypothesis that immigration and extinction rates for assemblages are predictable along environmental gradients, and that species are less prone to local extinction and more prone to colonize areas when they maintain high local abundances. The extinction process in local assemblages can be a highly ordered event leading to strong nested subset patterns, but immigration appears to be more stochastic.
- Research Article
25
- 10.1046/j.1365-2427.2001.00767.x
- Nov 1, 2001
- Freshwater Biology
1. A classic theory in biogeography predicts that high latitude communities are unstable. This may be because of decreased species richness or decreased environmental predictability and productivity towards the poles.2. We studied latitudinal patterns in long‐term community persistence of aquatic vascular plants in 112 Finnish lakes, situated within a 1000‐km range from the northernmost to the southernmost lake.3. Contrary to theoretical predictions, we found that the turnover rate of plant species in 45 years was inversely related to latitude. That is, plant communities in northern lakes were more persistent than communities in southern lakes. When we used multiple regression to find the best predictors of species turnover rate (TR), latitude was the only variable that was highly significantly related to species turnover rate. Area, species number, water transparency, pH and change in transparency did not notably explain the gradient observed.4. The latitudinal trend was mainly because of lower species immigration rates at higher latitudes, whereas extinction rate did not so strongly decrease with increasing latitude. Immigrations and extinctions in the lakes were not in balance: the species numbers between the 1930s and 1980s increased more strongly in the southern than northern lakes.5. We suggest that the inverse relationship between latitude and plant species TR in Finland is most probably caused by human influence on lakes, especially eutrophication and immigration of new species in southern latitudes. In addition, although species richness per lake did not decrease towards the north, the total species pool probably does, which means that in the north there are fewer species that can actually immigrate.
- Research Article
1
- 10.3354/meps13842
- Jan 1, 2021
- Marine Ecology Progress Series
The theory of island biogeography (TIB) predicts that species richness in isolated areas is determined by the processes of colonization and extinction, and, in turn, governed by island size and isolation. Metacommunity models extend the TIB, predicting that both habitat and species interactions are important drivers of community vital rates and structure, and that marine metacommunities will exhibit higher extinction/colonization rates relative to terrestrial ecosystems. Here we demonstrate that oceanic banks can be considered islands, and document how application of these theories advanced our understanding of the dynamics of these submarine islands following the fishery-induced collapse of predatory groundfish populations. We employed a 48 yr dataset of fish communities on 10 offshore banks of the Scotian Shelf, Northwest Atlantic Ocean to examine colonization and extinction rates before and after the collapse. Bank-specific colonization, extinction and turnover rates were quantified using the island R package to correct for imperfect detectability, inherent to all sampling of natural systems. Colonization and extinction events were briefly unbalanced following the predator collapse, and reflected in increases in species richness and turnover, most notably on the largest banks. However, over the longer term, a dynamic equilibrium of colonization and extinction events prevailed on 8 of the 10 banks. This resulted in a generally time-invariant species richness, and a negative relationship between species turnover and bank area, as predicted by theory. Our study provides support for the relevance of island biogeography and metacommunity theories in guiding exploration and understanding of the mechanisms governing marine community vital rates and structure.
- Research Article
32
- 10.1890/04-0352
- Jun 1, 2005
- Ecological Applications
As humans alter habitats worldwide, developing reliable methods of assessing biodiversity and community attributes of interest (e.g., species richness, turnover, and extinction rates) is important. Frequently, estimates of community‐level attributes are biased because the estimators make assumptions of the data that are violated; many published studies assume equal detectability across species, sites, or time. The accuracy of estimators of species richness and community‐level vital rates (e.g., extinction and colonization) can be increased by using probabilistic estimation methods, which do not assume that all species are detected, or that the data assume a particular statistical distribution.Using these estimation methods, we examined avian community dynamics in a fragmented tropical landscape using data from five years of a mark–release–recapture study. For the resident understory avifauna in each of five small (∼0.3–20 ha), isolated forest fragments in southern Costa Rica, we estimated species richness, rate of change in species richness, extinction and turnover rates of species, and the number of colonizing species over temporal scales of one month, one year, and two years. We expected that community dynamics would be higher in smaller fragments than in larger fragments, reflecting greater temporal variability of avian communities in relatively small habitat patches. Additionally, a selective logging operation was conducted at one of our sites during the midpoint of this study, which gave us the opportunity to examine how community‐level vital rates may reflect the effects of that perturbation.Our results demonstrate that avian communities in the larger fragments were more stable than those in the smaller fragments, and that the selectively logged fragment was the most unstable of all. We found that extinction rates were more similar across our sites than were colonization rates, and that the higher instability of the small fragments was due primarily to higher levels of colonization. Although our sample size (n = 5) precludes strong inference, our findings are consistent with the prediction of higher local dynamics within small fragments and after logging. Taken together, these findings suggest that smaller fragments are more dynamic over time, and that ecological processes and multitrophic relationships at these dynamic sites may be in a constant state of flux.
- Research Article
12
- 10.2307/3038083
- Dec 1, 1979
- Journal of Biogeography
We critically examine Wilcox's recent study which purports to prove dynamic equilibrium theory by demonstrating a species diversity-age relationship for lizard faunas on seventeen Baja California 'supersaturated' islands. We show both conceptual and technical problems with his analysis and propose an alternative explanation for his results. The proposition that species diversity results from balanced rates of species immigrations and extinctions was popularized by Preston (1962) and MacArthur & Wilson (1963, 1967). The experiments of Simberloff & Wilson (1970) and subsequently many others (see references in Simberloff, 1974) have been construed as conclusive support of this hypothesis. For several years, the hypothesis received little criticism. This 'dynamic equilibrium theory' states that species number remains constant because of observable but balanced species extinctions and immigrations, while species composition constantly changes. The existence of immigration, extinction, and 'turnover' (changes in species composition in the absence of changes in species number) is crucial to this theory. Lynch & Johnson (1974) criticized Diamond's (1969) conclusion that species 'turnover' is significant. Subsequently, Smith (1975) suggested that the high apparent rate of turnover was a problem of scale, and that as 'extinction' and 'immigration' has been defined, the equilibrium hypothesis was trivial. Simberloff (1976) recalculated his estimates of turnover for mangrove island arthropods and concluded that although turnover consisting of population extinctions occurred, far more of the original estimates represented either transient intra-population movement or death of individuals which never produced populations in the first place. Thus, the very experiments cited as the foundation for the dynamic equilibrium hypothesis were found not to evidence much turnover. Recently, Wilcox (1978) has contended that if 'non-equilibrium, supersaturated' island faunas are 'relaxing' (decreasing in species numbers), this can be construed as support for dynamic equilibrium theory. Were he to demonstrate such a relationship, it could be taken as support for Diamond's (1972) and Terborgh's (1975) ideas of long relaxation times. However, it has no bearing on dynamic equilibrium theory, since, as mentioned above, the critical requirement for dynamic equilibrium is observable, balanced rates of species immigrations and extinctions with species composition changes in the absence of changes in species number. Not only are Wilcox's (1978) conclusions irrelevant to the controversy involving dynamic equilibrium theory, but his analysis of the island agediversity relationship for lizard faunas on the islands in the Baja California region is beset with conceptual and technical problems that undermine its implication of long relaxation times. Given the omnipresent species-area relationship (Connor & McCoy, 1979) one would expect changes in island area resulting from sea level fluctuations to affect island 0305-0270/79/1200-0311 $02.00 ? 1979 Blackwell Scientific Publications 311 20 This content downloaded from 207.46.13.134 on Sun, 25 Sep 2016 05:00:36 UTC All use subject to http://about.jstor.org/terms 312 Stanley H. Faeth and Edward F. Connor species numbers. Diamond (1972), Terborgh (1975), Simpson (1974), and now Wilcox (1978) suggest that changes in species numbers resulting from such events do not occur instantaneously, but lag several thousand years behind changes in an island's physiographic characteristics, particularly area. Relaxation curves showing this trajectory of species loss over time (Terborgh, 1975) are usually a virtual mirror image of the familiar colonization curve (MacArthur & Wilson, 1963; Simberloff & Wilson, 1970). However, relaxation times are said to be extremely protracted, unlike those for colonization. Relaxing islands are thus supersaturated with species and are losing species in an inexorable return to the 'proper' number of species for a given island's area, and in Wilcox's example (1978), latitude. Wilcox presumes the islands in the Baja California region to be supersaturated, since when the islands were connected to the mainland the resident numbers of lizard species would have been some larger subset of the large mainland pool. Now isolated, the islands presumably retain more species than they 'should' have for their size and latitude. Specifically, Wilcox relates lizard species diversity to island age on seventeen Baja California land bridge islands, as well as to island area, elevation, isolation, distance from mainland, and latitude. He reasons that the observation of an inverse relationship between island age and diversity implies that young islands are still supersaturated and relaxing. He explores this relationship in three ways: (1) simple correlation between island area and diversity, (2) stepwise multiple regression techniques using species diversity as the dependent variable with island age and other physical parameters as explanatory variables, and (3) a type of partial correlation analysis where, after the effects of area and latitude are 'factored out,' residual species diversity is plotted against age. He then construes the plot of residual species diversity versus age as proof that species diversity is 'relaxing' toward an equilibrium value consistent with the present size and latitude of the island.
- Research Article
175
- 10.1073/pnas.73.11.4130
- Nov 1, 1976
- Proceedings of the National Academy of Sciences
Quantitative models of the species-area-distance relation, based on equilibria between immigration and extinction rates, have been tested against data for birds on 52 Solomon islands. Biologically reasonable models account for 98% of the variance in species number. The data are adequate to permit determination of immigration and extinction curves and the values of seven associated parameters. The resulting curves are very concave. Extinction rates vary almost exactly as the reciprocal of area, but the effect of area on immigration rates is slight. Recognition of major differences among species in immigration and extinction rates and in dispersal distances proves essential to a successful model.